Details

analyze7.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1

Compiler

Compiled 66 to 48 computations (27.3% saved)

sample2.4s (7.1%)

Symmetry

(sort cosTheta_i cosTheta_O)

(sort sinTheta_i sinTheta_O)

Results

2.3s

8256×

body

128

valid

Compiler

Compiled 159 to 115 computations (27.7% saved)

simplify51.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

913×	`times-frac_binary32`
551×	`associate-/l*_binary32`
460×	`associate-/l/_binary32`
362×	`associate-*l/_binary32`
312×	`associate-/r/_binary32`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	34
1	54	34
2	171	32
3	710	32
4	3631	32
5	4627	32
6	5261	32

prune5.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
▶	0.3b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Status

Error

Program

0.4b

(*.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

▶

0.3b

(/.f32 (*.f32 (exp.f32 (neg.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))) (/.f32 (*.f32 cosTheta_i cosTheta_O) v)) (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))

Compiler

Compiled 154 to 104 computations (32.5% saved)

localize57.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
✓	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	0.7b	(sinh.f32 (/.f32 1 v))

series39.0ms (0.1%)

Counts

4 → 24

Calls

4 calls:

13.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
12.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
8.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
7.0ms	(sinh.f32 (/.f32 1 v))

rewrite16.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-cbrt-cube_binary32`
19×	`add-exp-log_binary32`
9×	`*-un-lft-identity_binary32`
9×	`add-sqr-sqrt_binary32`
9×	`add-cube-cbrt_binary32`

Counts

4 → 77

Calls

4 calls:

6.0ms	(.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)
3.0ms	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
3.0ms	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
1.0ms	(sinh.f32 (/.f32 1 v))

simplify108.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

889×	`associate-/l*_binary32`
434×	`associate-*l/_binary32`
343×	`associate-/l/_binary32`
322×	`associate-*r/_binary32`
316×	`associate-/r*_binary32`

Counts

101 → 118

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	180	1396
1	428	1227
2	1461	1227
3	4514	1159
4	4805	1159
5	5000	1159
6	4999	1159
7	4940	1159

prune180.0ms (0.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	7	118
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	112	8	120

Error

0.1b

Counts

120 → 8

Alt Table

Status	Error	Program
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 (/.f32 cosTheta_i (sqrt.f32 v)) cosTheta_O) (sqrt.f32 v))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v)) (cbrt.f32 (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))) (cbrt.f32 (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (*.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))

Compiler

Compiled 3788 to 1785 computations (52.9% saved)

localize53.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))
	0.2b	(/.f32 (*.f32 sinTheta_i sinTheta_O) v)
✓	0.4b	(/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)))))
	0.7b	(sinh.f32 (/.f32 1 v))

series509.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

442.0ms

(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

67.0ms

(*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

rewrite29.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-cbrt-cube_binary32`
37×	`add-exp-log_binary32`
31×	`times-frac_binary32`
18×	`cbrt-unprod_binary32`
18×	`prod-exp_binary32`

Counts

2 → 81

Calls

2 calls:

12.0ms

(/.f32 (/.f32 cosTheta_i v) (*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))

8.0ms

(*.f32 v (*.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))

simplify118.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

543×	`times-frac_binary32`
446×	`associate-/r*_binary32`
424×	`associate-r_binary32`
411×	`associate-/l*_binary32`
346×	`associate-l_binary32`

Counts

165 → 164

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	361	8759
1	1170	7952
2	5082	7952

prune649.0ms (2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	206	7	213
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	210	11	221

Error

0.0b

Counts

221 → 11

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (.f32 (cbrt.f32 v) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)))))))
▶	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (/.f32 v (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (sqrt.f32 v)) v) (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (cbrt.f32 (/.f32 cosTheta_i v))) v) (/.f32 (cbrt.f32 (/.f32 cosTheta_i v)) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (.f32 (.f32 (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v))) (cbrt.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) v)))) (.f32 (*.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (*.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(.f32 cosTheta_O (/.f32 (/.f32 cosTheta_i v) (.f32 v (.f32 (.f32 (.f32 (.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v))))))

Compiler

Compiled 8894 to 4804 computations (46% saved)

localize68.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f32 1 (sqrt.f32 v))
✓	0.3b	(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))
	0.7b	(sinh.f32 (/.f32 1 v))
✓	0.8b	(/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))

series843.0ms (2.5%)

Counts

3 → 80

Calls

3 calls:

457.0ms

(/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))

373.0ms

(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))

13.0ms

(/.f32 1 (sqrt.f32 v))

rewrite871.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

8157×	`times-frac_binary32`
2785×	`*-un-lft-identity_binary32`
2785×	`add-sqr-sqrt_binary32`
2785×	`add-cube-cbrt_binary32`
1434×	`sqrt-prod_binary32`

Counts

3 → 2180

Calls

3 calls:

56.0ms

(/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))

13.0ms

(/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (*.f32 (exp.f32 (/.f32 (*.f32 sinTheta_i sinTheta_O) v)) (*.f32 2 (sinh.f32 (/.f32 1 v)))))

3.0ms

(/.f32 1 (sqrt.f32 v))

simplify3.0s (8.9%)

Algorithm

1×	egg-herbie

Rules

925×	`associate-/r/_binary32`
552×	`associate-/l/_binary32`
202×	`fma-def_binary32`
161×	`associate-/l*_binary32`
104×	`*-commutative_binary32`

Counts

2260 → 2076

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1448	145714
1	4609	143957
2	4996	143957
3	4976	143957

prune5.1s (15.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	2091	6	2097
Fresh	7	3	10
Picked	1	0	1
Done	0	0	0
Total	2099	9	2108

Error

0.0b

Counts

2108 → 9

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 1 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 (sqrt.f32 v))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 v (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 (sqrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (sqrt.f32 v) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (sqrt.f32 v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (*.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 (/.f32 1 (sqrt.f32 v))) (cbrt.f32 (/.f32 1 (sqrt.f32 v)))) (/.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (/.f32 cosTheta_i (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (cbrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (cbrt.f32 v) (/.f32 (/.f32 1 (sqrt.f32 v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
▶	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))))) (.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i (cbrt.f32 (sqrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (/.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v)))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (cbrt.f32 v) (/.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (.f32 2 (sinh.f32 (/.f32 1 v))))))))

Compiler

Compiled 103297 to 46005 computations (55.5% saved)

localize67.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f32 (*.f32 cosTheta_i cosTheta_O) v)
✓	0.4b	(log.f32 (sinh.f32 (/.f32 1 v)))
✓	0.6b	(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))
	0.7b	(sinh.f32 (/.f32 1 v))

series157.0ms (0.5%)

Counts

2 → 24

Calls

2 calls:

150.0ms	(log.f32 (sinh.f32 (/.f32 1 v)))
7.0ms	(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`log-prod_binary32`
5×	`*-un-lft-identity_binary32`
5×	`add-sqr-sqrt_binary32`
5×	`add-cube-cbrt_binary32`
4×	`exp-prod_binary32`

Counts

2 → 33

Calls

2 calls:

2.0ms	(exp.f32 (log.f32 (sinh.f32 (/.f32 1 v))))
2.0ms	(log.f32 (sinh.f32 (/.f32 1 v)))

simplify73.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

756×	`times-frac_binary32`
531×	`fma-neg_binary32`
349×	`associate-/r*_binary32`
314×	`fma-def_binary32`
254×	`associate-+l+_binary32`

Counts

57 → 70

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	101	913
1	200	864
2	429	864
3	1109	850
4	3151	707
5	4968	707
6	4930	707

prune308.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	118	1	119
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	119	9	128

Error

0.0b

Counts

128 → 9

Alt Table

Status	Error	Program
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 1 (/.f32 (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (sqrt.f32 (sqrt.f32 v))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 v (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 (sqrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (sqrt.f32 v) (/.f32 (.f32 (cbrt.f32 cosTheta_i) (cbrt.f32 cosTheta_i)) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (sqrt.f32 v) (/.f32 (/.f32 (cbrt.f32 cosTheta_i) (sqrt.f32 v)) (*.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (.f32 (.f32 (pow.f32 (cbrt.f32 (sinh.f32 (/.f32 1 v))) 2) (cbrt.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
✓	0.4b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (.f32 cosTheta_i cosTheta_O) v)) (.f32 (*.f32 (exp.f32 (log.f32 (sinh.f32 (/.f32 1 v)))) 2) v))
	0.5b	(.f32 cosTheta_O (.f32 (/.f32 (.f32 (cbrt.f32 (/.f32 1 (sqrt.f32 v))) (cbrt.f32 (/.f32 1 (sqrt.f32 v)))) (/.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (/.f32 cosTheta_i (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (cbrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (cbrt.f32 v) (/.f32 (/.f32 1 (sqrt.f32 v)) (.f32 2 (sinh.f32 (/.f32 1 v))))))))
	0.5b	(/.f32 (.f32 (exp.f32 (neg.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))) (/.f32 (/.f32 (.f32 cosTheta_i cosTheta_O) (.f32 (cbrt.f32 v) (cbrt.f32 v))) (cbrt.f32 v))) (.f32 (.f32 (sinh.f32 (/.f32 1 v)) 2) v))
	0.5b	(.f32 cosTheta_O (/.f32 (/.f32 1 (sqrt.f32 v)) (/.f32 v (/.f32 (/.f32 cosTheta_i (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 2 (expm1.f32 (log1p.f32 (sinh.f32 (/.f32 1 v))))))))))
	0.4b	(.f32 cosTheta_O (.f32 (/.f32 (/.f32 1 (sqrt.f32 v)) (.f32 (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v)) (.f32 (cbrt.f32 (sqrt.f32 v)) (cbrt.f32 (sqrt.f32 v))))) (.f32 (/.f32 1 v) (/.f32 (/.f32 cosTheta_i (cbrt.f32 (sqrt.f32 v))) (*.f32 2 (sinh.f32 (/.f32 1 v)))))))
	0.6b	(.f32 cosTheta_O (.f32 (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (.f32 (cbrt.f32 v) (cbrt.f32 v)) (/.f32 (.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v)))) (exp.f32 (/.f32 (.f32 sinTheta_i sinTheta_O) v))))) (/.f32 (sqrt.f32 (/.f32 1 (sqrt.f32 v))) (/.f32 (cbrt.f32 v) (/.f32 (cbrt.f32 (/.f32 cosTheta_i (sqrt.f32 v))) (.f32 2 (sinh.f32 (/.f32 1 v))))))))

Compiler

Compiled 4025 to 1987 computations (50.6% saved)

regimes18.2s (54.8%)

Accuracy

Total 0.3b remaining (68.6%)

Threshold costs 0.3b (68.6%)

Counts

1193 → 1

Compiler

Compiled 414916 to 280324 computations (32.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary32`
1×	`1-exp_binary32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	35
1	26	35
2	25	35

end371.0ms (1.1%)

Remove: (sort sinTheta_i sinTheta_O)
Compiler: Compiled 616 to 415 computations (32.6% saved)

Details

analyze7.0ms (0%)

sample2.4s (7.1%)

simplify51.0ms (0.2%)

prune5.0ms (0%)

localize57.0ms (0.2%)

series39.0ms (0.1%)

rewrite16.0ms (0%)

simplify108.0ms (0.3%)

prune180.0ms (0.5%)

localize53.0ms (0.2%)

series509.0ms (1.5%)

rewrite29.0ms (0.1%)

simplify118.0ms (0.4%)

prune649.0ms (2%)

localize68.0ms (0.2%)

series843.0ms (2.5%)

rewrite871.0ms (2.6%)

simplify3.0s (8.9%)

prune5.1s (15.3%)

localize67.0ms (0.2%)

series157.0ms (0.5%)

rewrite6.0ms (0%)

simplify73.0ms (0.2%)

prune308.0ms (0.9%)

regimes18.2s (54.8%)

simplify4.0ms (0%)

end371.0ms (1.1%)

Profiling